doc-src/TutorialI/Misc/Plus.thy
author berghofe
Wed, 07 May 2008 10:56:52 +0200
changeset 26803 0af0f674845d
parent 19249 86c73395c99b
child 27015 f8537d69f514
permissions -rw-r--r--
- Explicitely passed pred_subset_eq and pred_equals_eq as an argument to the to_set and to_pred attributes, because it is no longer applied automatically - Manually applied predicate1I in proof of accp_subset, because it is no longer part of the claset - Replaced psubset_def by less_le

(*<*)
theory Plus imports Main begin
(*>*)

text{*\noindent Define the following addition function *}

consts add :: "nat \<Rightarrow> nat \<Rightarrow> nat"
primrec
"add m 0 = m"
"add m (Suc n) = add (Suc m) n"

text{*\noindent and prove*}
(*<*)
lemma [simp]: "!m. add m n = m+n"
apply(induct_tac n)
by(auto)
(*>*)
lemma "add m n = m+n"
(*<*)
by(simp)

end
(*>*)